Question

The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick mass was 0.12 g, its speed before entering the branch was 221 m/s, and its penetration depth was 12 mm. If its speed was decreased at a uniform rate, what was the magnitude of the force of the branch on the toothpick?

Answer 1

Using 3rd kinematic equations:

V^2 = U^2 + 2*a*S

U = Initial velocity of toothpick = 221 m/sec

V = final speed of toothpick = 0 m/sec

S = Stopping distance = penetration depth = 12 mm = 0.012 m

So,

a = (V^2 - U^2)/(2*S)

a = (0 - 221^2)/(2*0.012)

a = -2035041.67 m/sec^2

(-ve sign means de-acceleration)

Now from newton's 2nd law force exerted on toothpick will be

Fnet = m*a

m = mass of toothpick = 0.12 gm = 0.12*10^-3 kg

So,

Fnet = 0.12*10^-3*(-2035041.67)

Fnet = -244.2 N

Magnitude of force = |Fnet| = 244.2 N

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